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Not my point… and you know it. My point is that even if we consider that proven theorems are known facts, we still dont know if hypercomputers are infeasible. We know, however, that i’ll never write python code that decides Validity because it is not (classically) decidable. But we have no theorems on the impossibility of hypercomputation.
Right, validity is semidecidable, just like the halting problem.
We might never know for certain that any natural law is true, we might never be certain that that oracle actually solves validity. But that doesnt prevent the oracle from working. My point is that its existence is possible, not that we will ever be able to trust it.
Besides, we dont know that the physical laws we work with today are true, but we nevetheless use them for practical purpuses all the time.
Turing machines can’t exist, either.
Oh no! You got me there!
Why do you need uncountable infinities for hypercomputers, though?. I see that Martin Davis criticism has to do with that approach, and I agree this approach seems silly. But, it doesnt seem to cover all potential fronts for hypercomputers. Im not talking about current approaches to quantum computing either. What if some yet unknown physical law makes arrangements of particles somehow solve the first order logic validity problem, which is also not in R? Doesnt involve uncountable infinity at all. Again, im not saying its possible, just that theres no purely logical proof of impossibility, thats all.
church-turing is a a thesis, not a logical theorem. You pointed me to a proof that the halting problem is unsolvable by a Turing Machine, not that hypercomputers are impossible.
The critic Martin Davis mentioned in wikipedia has an article criticizing a kind of attempt at showing the feasibility of hypercomputers. Thats fine. If there was a well-known logical proof of its unfeasibility, his task would be much simpler though. The purely logical argument hasnt been made as far as i know and as far as you were able to show.
The diagonalization argument you pointed me to is about the uncomputability of the halting problem. I know about it, but it just proves that no turing machine can solve the halting problem. Hypercomputers are supposed to NOT be turing machines, so theres no proof of the impossibility of hypercomputers to be found there.
I know diagonalization proofs, they dont prove what you say they prove. Cite any computer science source stating that the existence of hypercomputers are logically impossible. If you keep saying it follows from some diagonalization argument without showing how or citing sources ill move on from this.
why having a paywall if that scenario enables people to become absolute subservient machines deprived of any subjectivity?
…I never said they are not.
The incompleteness theorem says that a consistent axiomatic formal system satisfying some conditions cannot be complete, so the universe as a formal system (supposed consistent, complete, expressive enough, …) cannot be axiomatized.
external oracles
What do you mean external?
The possibility of using physical phenomena as oracles for solving classically uncomputable problems in the real world is an open question. If you think this is logically as impossible as a four sided triangle you should give sources for this claim, not just some vague statements involving the incompleteness theorem. Prove this logical impossibility or give sources, thats all im asking.
Who says you cant take a first order logic sentence, codify it as a particular arrangement of certain particles and determine if the sentence was valid by observing how the particles behave? Some undiscovered physical phenomenon might make this possible… who knows. It would make possible the making of a real world machine that surpasses the turing machine in computability, no? How is this like a four sided triangle? The four sided triangle is logically impossible, but a hypercomputer is logically possible. The question is whether it is also physically possible, which is an open question.